Delft University of Technology
Evaluation of relative density effects on liquefiable sands using PM4Sand model
Laera, A.; Vilhar, G.; Brasile, S.; Brinkgreve, Ronald
Publication date 2019
Document Version Final published version
Citation (APA)
Laera, A., Vilhar, G., Brasile, S., & Brinkgreve, R. (2019). Evaluation of relative density effects on liquefiable sands using PM4Sand model. Poster session presented at 7th International Conference on Earthquake Geotechnical Engineering, Rome, Italy.
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Evaluation of relative density effects on liquefiable sands using PM4Sand model
A. Laera1,2, G. Vilhar1, S. Brasile1, R.B.J. Brinkgreve3
1Plaxis bv, a Bentley Systems Company, Delft, The Netherlands - 2Department of Civil, Environmental, Land, Building Engineering and Chemistry,
Politecnico di Bari, Bari, Italy - 3Delft University of Technology, Delft, The Netherlands
To simulate the behaviour of saturated sands under cyclic loading, the PM4Sand constitutive model (version 3.1) formulated by Boulanger & Ziotopoulou [1], is used. The model can realistically reproduce the pore pressure build-up, accumulation of strain as well as triggering of liquefaction. The effect of dif-ferent relative densities on liquefaction resistance is evaluated by comparing the results of a site response analysis performed on a soil column character-ized by a saturated sand layer and subjected to given earthquake signals. The analyses are performed using the finite element code PLAXIS.
Aim
To show the role that the relative density in the PM4Sand model plays on the liquefaction potential, through:
• cyclic DSS tests using a single stress point constitutive driver;
• finite element-based one-dimensional site response analyses.
The constitutive model
The PM4Sand model is an elasto-plastic, stress-ratio-controlled, critical state compatible, bounding surface plasticity model, based on the Dafalias -Manzari model [2]. The PM4Sand model has become available in the ge-otechnical finite element software PLAXIS 2D [3].
Characteristics:
• 4 surfaces: the yield, bounding, dilation and critical state surface;
• current state defined by ξR (relative state parameter index equal to DR -
DR, CS), evolving with the mean effective stress and/or void ratio;
• primary parameters to be calibrated are the shear modulus coefficient
G0, the relative density DR, the contraction rate parameter hp0;
• default values are assumed for the secondary parameters.
Effect of the relative density on Cyclic DSS tests
• undrained stress-controlled cyclic DSS tests;
• anisotropic consolidation with K0 equal to 0.5;
• initial vertical stress ’v equal to 100 kPa;
• different shear stress amplitude for different DR (Table 1), equal to the
value that triggers liquefaction at 3% shear strain, applying 15 uniform cycles.
Effect of the relative density in a one-dimensional site response
analysis
• soil column with tied degrees of freedom as lateral boundary condition;
• 3 different outcrop motions (Loma Prieta, Kalamata and Northridge
earthquakes): amax = 0.3g, different frequency content and duration.
Results and conclusion
• the model is capable of accumulating shear strains and excess pore
pressures while the effective vertical stress tends to zero, leading to
liq-uefaction after 15 stress-controlled loading cycles (Figure 1);
• generated butterfly shape during final loops, when the stress state
moves up and down along the failure envelope (Figure 1);
• the cyclic resistance ratio increases with increasing DR (Figure 1);
• the loose and medium loose sands liquefy in the case of all three
select-ed earthquakes (Figure 2);
• the evolution of the pore pressure ratio, ru, shows that the onset of
liq-uefaction occurs at different times based on the characteristics of the earthquake, but it seems to be independent from the relative density of the saturated sand (Figure 3);
• the dense sand does not liquefy: after an initial increase of ru, the
ex-cess pore pressures are partially dissipated (Figures 2 and 3).
Figure 2 - Maximum pore pressure ratio contours for Loma Prieta earthquake (a, d, g), Kalamata earth-quake (b, e, h) and Northridge earthearth-quake (c, f, i) for different relative densities.
Figure 3 - Comparison of the pore pressure ratio evolution for loose (left) and medium loose (center) and dense (right) sand, for different earthquake recordings.
Figure 1 - Results from cyclic DSS test for 3 different relative densities. Shear stress vs. shear strain (a), pore pressure vs. shear strain (b), shear stress vs. vertical effective stress (c).
References
[1] Boulanger, R.W. & Ziotopoulou, K. 2017. PM4Sand (Version 3.1): A sand plasticity model for earthquake engineering applications. Report No. UCD/CGM-17/01, Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California, Davis, CA.
[2] Dafalias, Y.F. & Manzari, M.T. 2004. Simple plasticity sand model ac-counting for fabric change effects. Journal of Engineering Mechanics, ASCE, 130(6), 622-634.
[3] Vilhar, G., Laera, A., Foria, F., Gupta, A. & Brinkgreve, R.B.J. 2018. Im-plementation, Validation, and Application of PM4Sand Model in PLAXIS. GEESD V. Geotechnical Special Publication. GSP 292. 200-211.
DR (N1)60 G0 CRRM=7.5, 1atm hp0
0.35 6 476 0.090 0.53
0.55 14 677 0.147 0.40
0.75 26 890 0.312 0.64
